On Saturday Derek picked pears from 32 trees. His picked average of 17 pears per tree. Sunday he picked more pears averaging 12 pears per tree. Over the whole weekend he picked an average of 14 pears per tree. How many trees did Derek pick from on Sunday? Please help with this question. I can't seem to get the right answer although I know it has something to do with the mean. Thanks
It has to do with the mean, in that the total pears picked on a day is the number of trees times the average picked per tree.
If he picked n trees on Sunday, his total pear count is
32*17 + n*12 = (32+n)*14
n = 48
Well, it seems like Derek had a very fruitful weekend! Let's break down the problem.
On Saturday, Derek picked pears from 32 trees, with an average of 17 pears per tree. So he picked a total of 32 trees * 17 pears/tree = 544 pears on Saturday.
Now, let's assume that on Sunday, Derek picked pears from "x" number of trees. Since he picked an average of 12 pears per tree, the total number of pears he picked on Sunday is x trees * 12 pears/tree = 12x pears.
For the whole weekend, Derek picked an average of 14 pears per tree. So the total number of pears he picked over the whole weekend is (544 pears + 12x pears) divided by (32 trees + x trees), which is equal to 14 pears per tree.
We can set up an equation to solve for "x":
(544 pears + 12x pears)/(32 trees + x trees) = 14 pears per tree
Now, let's solve it!
544 + 12x = 14(32 + x)
544 + 12x = 448 + 14x
544 - 448 = 14x - 12x
96 = 2x
x = 48
So, Derek picked pears from 48 trees on Sunday. I hope that puts a smile on your face!
To solve this problem, we can set up an equation using the given information.
Let's say Derek picked pears from "x" trees on Sunday.
According to the information given:
On Saturday, Derek picked pears from 32 trees, with an average of 17 pears per tree.
So, the total number of pears picked on Saturday = 32 × 17.
On Sunday, Derek picked pears from "x" trees, with an average of 12 pears per tree.
So, the total number of pears picked on Sunday = x × 12.
Over the whole weekend, Derek picked an average of 14 pears per tree.
The total number of pears picked over the weekend = (32 + x) × 14.
According to the problem, the total number of pears picked on Saturday plus the total number of pears picked on Sunday equals the total number of pears picked over the weekend:
(32 × 17) + (x × 12) = (32 + x) × 14.
To find the value of "x" (number of trees picked on Sunday), we can solve this equation.
First, let's simplify the equation:
544 + 12x = 448 + 14x.
Next, let's rearrange the terms:
12x - 14x = 448 - 544.
Combine the like terms:
-2x = -96.
Now, divide both sides of the equation by -2 to solve for "x":
x = (-96) / (-2).
Simplifying:
x = 48.
Therefore, Derek picked pears from 48 trees on Sunday.
To solve this problem, we can use the concept of weighted averages.
Let's first analyze the information given in the problem:
On Saturday, Derek picked pears from 32 trees with an average of 17 pears per tree. This means he picked a total of 32 * 17 = 544 pears on Saturday.
On Sunday, Derek picked more pears with an average of 12 pears per tree. Let's say he picked from 'x' number of trees on Sunday. This means he picked a total of x * 12 = 12x pears on Sunday.
Over the whole weekend, Derek picked an average of 14 pears per tree. This means the total pears picked over the weekend is (32 + x) * 14.
Now, we can set up an equation to find the value of 'x':
(544 + 12x) = (32 + x) * 14
Let's solve this equation step-by-step:
544 + 12x = 448 + 14x [Distribute the 14 on the right side]
544 - 448 = 14x - 12x [Subtract 448 from both sides]
96 = 2x [Combine like terms]
x = 48
Therefore, Derek picked from 48 trees on Sunday.
To summarize: Derek picked from a total of 48 trees on Sunday.